Abstract

Previous attempts to analytically describe wave reflection and transmission at surface penetrating structures have neglected losses due to flow expansion, contraction, and skin drag along the structure boundaries (Black and Mei, 1970; Ijima, et al., 1972). The model described in this study includes these effects and allows for the inclusion of a dissipative medium such as rubble or closely spaced piles in the region beneath the structure. The problem of a fixed, two-dimensional structure in a train of monochromatic incident waves is modeled, as shown in Figure 1. The solution allows for 1) variable structure length and draft, 2) different depths in the regions fore, aft, and beneath the structure, 3) variable wave amplitude and period, and 4) turbulent and inertial damping in the region beneath the structure. An equivalent work technique is applied to linearize the damping beneath the structure, yielding a potential flow problem in all three regions. Amplitudes for the resulting series of eigenfunctions in each region are determined by matching pressure and horizontal mass flux at the region interfaces, orthogonalizing these expressions over the depth, and simultaneously solving the resulting equations to yield complex reflection and transmission coefficients. Complex horizontal and vertical force coefficients for the structure are also determined from the integrated Bernoulli equation. The solution technique is computationally efficient. In general, five modes in the eigen series provide satisfactory convergence for the various hydrodynamic parameters. Approximately six-tenths of a computer system second are required to solve for a single wave-structure condition. The results compare favorably with variational methods used by others.